Session P1: Poster Session: General Fluid Dynamics

The Effect of Large Scale Freestream Turbulence on Heat Transfer in Stagnating Flow

Water tunnel experiments have been performed to investigate a general mechanistic model [1] for heat transfer augmentation by large scale freestream turbulence at a stagnation point. Time-resolved Digital Particle Image Velocimetry was used to measure velocity fields and calculate both integral length scale and turbulence intensity in the vicinity of the stagnation point. Time resolved surface heat flux measurements were made simultaneously using a novel thin film heat flux sensor fabricated and calibrated in-house. Varying levels of freestream turbulence were generated using grids at several positions upstream of the stagnation test apparatus. Laminar and turbulent experiments were conducted at Reynolds numbers of 4762, 9525, and 14287 based on the bar width of the turbulence grid. Experimental results for the heat transfer coefficient agree well with results from the general model using only experimental turbulence characteristics. \newline [1] Nix, A.C. ``Experiments on the Physical Mechanism of Heat Transfer Augmentation by Freestream Turbulence at a Cylinder Stagnation Point'' Proceedings of GT2005 ASME Turbo Expo 2005. GT-2005-68616. June 6-9, 2005   

Stability Study of Rayleigh-Taylor Instability in the Presence of Flow

The effect of a radially varying parallel equilibrium flow on the stability of Rayleigh- Taylor (RT) instability is studied analytically in the presence of a sheared magnetic field. It is shown that the parallel flow curvature can completely stabilize the RT mode. The flow curvature also has a robust effect on the radial structure of the mode. Possible implications of these theoretical findings to recent experiments are also discussed.   

Mitigation of R-T and R-M instabilities in ICF targets through the use of high-Z overcoats and prepulses

We report on simulations of direct-drive ICF targets incorporating a thin, high-Z (metallic) overcoat. The overcoat converts incident UV laser energy to soft X-rays, which produce a higher ablation velocity and consequently a lower Richtmeyer-Meshkov instability amplitude. The reduced R-M amplitude results in a smaller seed for the Rayleigh-Taylor instability that occurs during target acceleration, which leads to a more stable target implosion. The R-T growth rate is also reduced due to the shaping of the ablator density (and adiabat) by the penetration of X-rays into the ablator. Similar adiabat shaping can also be produced by the use of laser prepulses or spikes, as has been widely reported. Here we explore new target designs that combine the use of overcoats with laser spikes in an attempt to both reduce the seed for the R-T instability as well as its growth rate. We examine in detail as well the situations in which both overcoats and prepulses can increase target instability in order to arrive at a set of constraints for optimal target design.   

Surface tension in incompressible Rayleigh-Taylor mixing flow

We study the effect of surface tension on the incompressible Rayleigh-Taylor instability. We modify Goncharov's local analysis [1] to consider the surface tension effect on the Rayleigh-Taylor bubble velocity. The surface tension damps the linear instability and reduces the nonlinear terminal bubble velocity. We summarize the development of a finite-volume, particle-level-set, two-phase flow solver with an adaptive Cartesian mesh, and results from convergence and validation studies of this two-phase flow solver are provided. We use this code to simulate the single-mode, viscous Rayleigh-Taylor instability with surface tension, and good agreement in terminal bubble velocity is found when compared with analytic results. We also simulate the immiscible Rayleigh-Taylor instability with random initial perturbations. The ensuing mixing flow is characterized by the effective mixing rate and the flow anisotropy. Surface tension tends to reduce the effective mixing rate and homogenizes the Rayleigh-Taylor mixing flow. Finally we provide a scaling argument for detecting the onset of the quadratic, self-similar Rayleigh-Taylor growth.   

Marangoni Instabilities in Small Circular Containers under Microgravity

Circular containers of various aspect ratios \textbf{\textit{a}} with flat free upper liquid surfaces were heated from below under microgravity to study the Marangoni instability. We realized ``liquid lateral sidewalls'' for the containers to come near to the ``slippery sidewalls'' introduced earlier by theory. The flow structure was visualized by aluminium flakes and recorded on videotape. Different perfect flow structures (azimuthal and radial wave numbers) were observed in the containers with \textbf{\textit{a}} = 0.5, 0.75, 1.0, 1.5, 2.0, 4.0 and 5.0. The observed scenario compares qualitatively well with the stability curves calculated by other authors. Frequent switching between modes (2,1) and (1,1) was observed in the container with \textbf{\textit{a}} = 2 at supercritical \textbf{\textit{Ma}}.   

Shear Flow Instabilities in the Presence of Flow Curvature

A nonlocal theory of the electrostatic parallel velocity shear instability in a three-dimensional slab with a uniformly sheared magnetic field has been developed. It is shown that in the limit of a weak parallel velocity gradient, the linear growth rate can be increased depending upon the direction of the magnetic shear with respect to the radial curvature of the parallel velocity profile $(d^2v/dx^2)$. When these parameters have the same sign, the growth rate can actually be stronger than in the limit of no magnetic shear. In this limit of increased instability, the eigenmode is broadened, thus producing enhanced transport. For strong parallel velocity gradients that are more typical of flows in tokamaks, the effect of the varying Doppler shift becomes more prominent on the stability of the mode, the net result being that the sensitivity of the growth rates on the sign of the magnetic shear becomes insignificant. This effect, however, is effectively offset when a finite density gradient is included. When the density scale length is of order the scale length of v, the growth rate is moderately reduced, but becomes dependent again upon the sign of the magnetic shear.   

Heat/Fluid Flow Performance of Binary Gas Mixtures Formed with Helium Across Parallel-Plate Channels

The present study examines the trade-off between heat transfer enhancement and pressure drop increments caused by the flow of laminar binary gases in parallel-plate channels. Helium is the primary gas and carbon dioxide, methane, nitrogen, oxygen and xenon are the secondary gases. From fluid physics, two thermophysical properties: viscosity and density affect the gas flow, whereas four thermophysical properties: viscosity, density, thermal conductivity, and heat capacity at constant pressure influence the forced convection. From physical-chemistry, the collection of four thermophysical properties depends on temperature, pressure and molar gas composition. The simultaneous development of laminar velocity and temperature of each binary gas mixture is predicted using the finite volume method for two Reynolds numbers based on hydraulic diameter, i.e., 1000 and 2000. The two target parameters are the total heat transfer or mean convection coefficient and the pressure drop. The beneficial connectedness of the two target parameters changing with the molar gas composition is reported in terms of a proper figure-of-merit, the heat/fluid flow performance parameter for the two Reynolds numbers.   

The Performance of Fluid Displacements in Heterogeneous Reservoirs

The injection of one fluid to displace another in a heterogeneous porous medium is the basis of many industrial processes such as Enhanced Oil Recovery (EOR) and the remediation of contaminated aquifers. When the results are presented in scaled format, it is then possible to use the data acquired on a given system (i.e. laboratory system) to predict the behavior of another similar system, the one of actual interest, the prototype. The study followed a rigorous procedure of inspectional analysis to derive the independent dimensionless scaling groups that describe immiscible displacements in heterogeneous reservoirs with constant porosity and dip angle. Fine-mesh numerical simulations were then performed in order to reveal the functional relationships between the scaling groups describing the displacement and the fractional oil recovery obtained from such displacement. The results obtained from several well configurations will be presented, which includes the use of several horizontal-vertical well combinations. These relationships can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. In addition, they provide the condition under which a given well configuration may yield better recovery performance.   

Uniform Bubbles Generated in the Simple Microfluidic Device

We construct a bubble generator by two tiny capillary tubes embedded in a square capillary tube which is the same as the double emulsion set up from Weitz lab (Science \textbf{308} 537 (2005)). Bubbles generated in this device are uniform in size. The size is a function of the distance between two capillary tubing, the orfice of the tubing and the flow speed of the air jet and the surrounding fluid. The bubbles are stabilized with surfactant and organize themselves into foam of uniform size distribution. We put polymer in the surrounding fluid and crosslink it. The solidified foam shows interconnectivity between the voids.   

Combined PIV-LIF measurements in a turbulent liquid-liquid Taylor Couette flow.

We are building up an experiment to study the dispersion process of two immiscible fluids in a turbulent Taylor-Couette shear-flow. The two cylinders (radius $r_i=110$mm and $r_o=120$mm with a gap height of $180$mm) are counterrotating at a maximum speed of $30$rad/s. The liquids are a low-viscous oil and a refractive index matched $NaI$-water solution to get transparent dispersions. The viscosity ratio is close to one and the density ratio is $1.6$. Different phase ratios are used in the experiments. When the two cylinders are counterrotating, a dispersion is formed above a certain threshold in speed, with a sharp increase in the torque measured on the inner cylinder. Again lowering the speed, hysteresis is present in our system. Since we do not use surfactants, the dispersions are not stable: a balance between turbulent breakup and coalescence gives a certain droplet size distribution. We study the dynamics of the droplets by LIF: the oil phase is marked with a fluorescent dye, the flow is illuminated with a Nd:YAG laser, and imaged using a low-pass filter to only catch the fluorescence light. We are also measuring the 3 components of the velocity field in a plane normal to the mean flow by stereoscopic PIV, and we will compare the dilute two-phase flow with a single-phase flow.   

Asymptotic Analysis of the Selective Dip-Coating of Non-Newtonian Fluids onto Chemically Micropatterned Surfaces

The dip coating of a chemically micropatterned surface bearing a wetting vertical strip surrounded by non-wetting regions is analyzed for a non-Newtonian power-law fluid. The microscopic surface heterogeneity selectively confines liquid to the narrow strip. Asymptotic matching is used to determine the thickness of the liquid film deposited on the 10 $\mu$m-scale strip at small capillary numbers. In the absence of an imposed length scale on uniformly wetting surfaces, the governing length scale in the dynamic meniscus is found from a balance of viscous and capillary forces and depends on fluid properties. The power-law dependence of the viscosity can therefore have a considerable effect on the coating process. On micropatterned surfaces the effect of the power-law index on the thickness of the entrained liquid film is greatly reduced because of the dominant effect of the lateral fluid confinement by micropatterning, which imposes a geometric length scale that replaces the dynamic capillary length in the analysis. This greatly diminished effect of power-law behavior is therefore also expected to hold for other non-Newtonian fluids coated onto micropatterned surfaces because the governing (geometric) length scale is independent of fluid properties.   

Modeling rotational instabilities in aluminum reduction cells

Industrial production aluminum is achieved by means of electrolysis in aluminum reduction cells, in which a shallow electrolytic bath layer floats on top of liquid aluminum. Perturbations of the interface may initiate unstable waves by disturbing the electrolysis current, thus giving rise to a magnetic force through the action of the background magnetic field. Long-waves tend to turn into a rotating wave, whose essential driving mechanism is fairly well understood. However, the flow in a cell is observed to be also dominated by a few large scale vortices whose dimensions and intensity depends on the configuration of the magnetic force due to the background magnetic field. We have extended the stability analysis of interfacial waves to rotating fluids in a hypothetical cylindrical cell. Our model predicts three types of instabilities: (1) rotating waves altered by the global rotation; (2) axisymmetric circular waves; and (3) axisymmetric circular non-oscillatory disturbances. The latter type is expected to be the most unstable. We validate some of the predictions with numerical simulations.   

Alternating Waves in Electroconvection of Nematic Liquid Crystals

We present the results of pattern formation in electroconvection of liquid crystal 4-ethyl-2-fluoro-4$'$-[2-(trans-4-pentylclohexyl)-ethyl]biphenyl (I52) with planar alignment. The pattern was a function of three control parameters: applied ac voltage, driving frequency and electrical conductivity. Over certain range of conductivity, the initial transition (supercritical Hopf bifurcation) leads to right and left traveling zig and zag rolls .Time evolution of spatial Fourier transform (FT) of a series of these images with the sampling rate greater than Hopf frequency and taken under same controlled parameters were studied. To demodulate zig/zag rolls, the region around \textbf{k}$_{n }$( the wave vector of a given mode) of interest at one quarter of the FT was taken setting remainder of the FTs to zero. Taking the index of the maximum FT value at that region as the reference point, again this region was separated into four parts and redistributed at four corners. The absolute value of the inverse FT of the modified function gives the required envelope. The temporal variation of the amplitudes of these envelopes is periodic between standing zig and zag modes which are consistent with the theoretical predictions*. Supported by NSF-DMS0407418. \newline *G. Dangelmayr and I. Opera. Mol. Cryst., Liq. Cryst., 413:2241, 2004   

Complex dynamics near the threshold of convection for a water-ethanol mixture in a shallow cylinder

Direct numerical simulations of binary convection in shallow 3D cells are presented. The full unsteady convection equations in cylindrical coordinates are solved with an accurate spectral solver. We use a mixture with separation ratio $S = -0.09$, Prandtl number $\sigma= 24$ and Lewis number $\tau= 0.008$ and we analyse pattern formation near the onset of convection in a cylinder of aspect ratio $\Gamma=11$, motivated by the available experimental results in this geometry. The critical Rayleigh number ($R$), frequency and azimuthal mode ($n=1$) obtained in current DNS computations perfectly matches former linear stability analyses. During the nearly linear transient growth, the pattern consists of radially travelling waves, nearly standing in the azimuthal direction. As convection evolves, simulations for slightly subcritical and supercritical values of $R$ reveal differences in the dynamics. For slightly subcritical or supercritical values of $R$, repeated bursts of convection takes place. When the amplitude of convection is growing, the system suddenly collapses to a small-amplitude state that may grow aperiodically or eventually die. For supercritical values of $R$, the Nusselt number progressively increases and a blob of disordered convection forms around the cell centre slowly growing and reaching the cylinder walls, leading to a quasi steady state consisting of convection rolls coexisting with a small region of quiescent fluid.   

Turbulent convection at high Rayleigh numbers and aspect ratio 4

We report measurements of the Nusselt number, $Nu$, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was $Ra = 2 \times 10^{13}$. Except for the last half a decade or so of $Ra$, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the log$Nu$-log$Ra$ slope saturates at a value close to 1/3, as observed previously by us in experiments of smaller aspect ratios. The increasing slope over the last half a decade of $Ra$ is inconclusive because the corresponding conditions are non-Boussinesq. Finally, we report a modified scaling relation between the plume advection frequency and ${Ra}$ that collapses data for different aspect ratios. At moderately high Rayleigh numbers the mean wind can no longer be considered coherent over the entire container as indicated by the lack of long-time correlation between opposite wall sensors.   

The Explanation of the Pauli Exclusion Principle

Using the principles of the Vortex Theory, the construction of the alpha particle, and the theory that the nucleus is constructed out of alpha particles, the explanation of the Pauli Exclusion Principle is explained. If protons and electrons are connected to each other via fourth dimensional vortices, they spin in opposite directions. Since the alpha particle possesses two protons possessing opposite spins, their electrons also possess opposite spins. With a nucleus constructed out of alpha particles, all paired electrons in shells and sub-shells will spin in opposite directions. 1. Victor Vasiliev, Russell Moon. Controversy surrounding the Experiment conducted to prove the Vortex Theory, 2006 8th Annual Meeting of the Northwest Section, May 18-20, 2006, University of Puget Sound, Tacoma, Washington, USA, Abstract C1.00009. 2. Russell Moon. To the Photon Acceleration Effect, 2006 Texas Section APS/AAPT/SPS Joint Spring Meeting, Thursday--Saturday, March 23--25, 2006; San Angelo, Texas, Abstract: POS.00008. 3. Russell Moon, Fabian Calvo, Victor Vasiliev. The Neutral Pentaquark, 2006 APS March Meeting, March 13-17, Baltimore, MD, USA, Session Q1: GENERAL POSTER SESSION, Abstract Q1.00147.   

Coherent structure identification and tracking in turbulent jets

A pattern recognition algorithm is proposed to identify and track spatio-temporal regions of collective laminar, vortical and helical motion. This algorithm is applied to turbulent jet data at $Re=3600$ including incompressible and $Ma=0.9$ flow. Thus, mechanisms of mixing and noise production are clarified in the most active area of the potential core breakdown employing coherent structure analysis. Correlations are identified between vortex sound sources and coherent structure dynamics.   

Is Hideki Yukawa's explanation of the strong force correct?

Reexamining Hideki Yukawa's explanation of the strong force using the principles of the Quark Theory and the Vortex Theory, it was discovered that it is possible for a virtual particle to be passed back and forth between the proton and the neutron. This discovery creates a new and revolutionary explanation of the strong force of nature. The creation of the strong force appears to be the combination of four processes at work in the nucleus: virtual particles, intrinsic magnetism, ``nuclear gravity'', and gluons. 1. V.V. Vasiliev, R.G. Moon, The bases of the vortex theory, Book of abstracts The 53 International Meeting on Nuclear Spectroscopy and Nuclear structure St. Petersburg, Russia, 2003, p.251. 2. H. Yukawa, Tabibito, (World Scientific, Singapore, 1982), p. 190-202. 3. K. Gridnev, V.V. Vasiliev, R.G. Moon, The Photon Acceleration Effect, Book of abstracts, OMEGA 5 -- Symposium on Origin of Matter and Evolution of Galaxies, Nov 8-11, University of Tokyo, Tokyo Japan. 4. R.G. Moon, V.V. Vasiliev. Explanation of the Conservation of Lepton Number, Book of abstracts LV. National Conference on Nuclear Physics, Frontiers in the Physics of Nucleus, June 28-July 1, 2005, Saint-Petersburg, Russia, 2005, p. 347.5. .   

Laboratory Study of Coastal-Trapped Wave (CTW) Interaction with Submarine Canyon

CTW propagation along the continental slope and its subsequent interaction with the submarine canyon was investigated experimentally. Our observations demonstrated that CTW propagates along the continental slope with the strongest currents being concentrated near the shelf break. The topographic irregularity was strong enough to promote wave scattering. Flow characteristics in the canyon were found to be sensitive to the relative value of the Burger number. When the latter was very large (strong stratification), no variations in the wave spatial structure were observed in the canyon region. The scattering effect becomes significant at moderate values of the Burger number (of the order of unity). It was shown that stratification can eliminate backward propagating modes and limit the number of transmitted modes, forcing the flow to generate highly-energetic evanescent modes in order to adjust to the variations of the topography. Evanescent modes, which are characterized by large amplitudes and small length scales, cause amplification of the velocity field and strong variation in the spatial structure of the flow in the vicinity of the scattering region. Eventually strong mesoscale flows are generated in the form of a cyclonic eddy trapped inside the canyon region influencing the transport of nutrients and pollutants in the coastal region.   

Modulated point vortex couples on a beta-plane: dynamics and chaotic advection

The dynamics of modulated point vortex couples on a beta-plane is investigated for arbitrary ratios of the vortex strength. The motion is analysed in terms of an angle and a location dependent potential and the structural changes in their shape. The location dependent potential is best suited for understanding different types vortex orbits. It is shown to be two-valued in a range of parameters, a feature which leads to the appearance of orbits with spikes, in spite of the integrability of the problem. The advection dynamics in this modulated two-vortex problem is chaotic. We point out a transition from closed to open chaotic advection implying that the transport properties of the flow might drastically be altered by changing some parameters or the initial conditions. The open case, characterized by a permanent entrainment and detrainement of particles around the vortices, is interpreted in terms of an invariant chaotic saddle of the Lagrangian dynamics, while the dynamics of the closed case, with a permanently trapped area of the fluid, is governed by a chaotic region and interwoven KAM tori.   

Forced-dissipative shallow water turbulence on the sphere

Geostrophic turbulence and zonal jet formation is examined in the context of the forced-dissipative shallow water equations in spherical geometry. A number of interesting results are presented and compared with previous work on forced-dissipative barotropic turbulence, in both planar and spherical geometries, and freely-decaying shallow water turbulence: (1) Equilibrium states in the forced-dissipative problem exhibit various sensitivities to forcing and large scale dissipation; in particular, for a given total energy the steadiness of zonal jets depends crucially on the strength of forcing and dissipation. (2) Radiative relaxation, a natural dissipation mechanism for planetary atmospheres, leads to equatorial jets (both retrograde and prograde) which are significantly stronger than jets in midlatitudes. (3) A new regime is obtained at small deformation radius (comparable to that of the Jovian atmosphere) in which zonal jets are confined to low latitudes while the high-latitude flow remains approximately isotropic with anomalous intensity of anticyclonic motion.   

Stability analysis of laminar flume flow coupled with sediment transport

The ubiquitous formation of regular sedimentary patterns in rivers, such as bars, braids and meanders, is of prime interest to the geomorphologist. Fluid dynamics can provide critical insight into these phenomena. Numerous theoretical advances and laboratory experiments indicate that these patterns do not simply reflect a flow instability or a coherent turbulent structure. Instead, their formation results from the interaction between a surface flow and an erodible substrate, through an erosion law. Indeed, the interface separating the sediment layer from water is found to be unstable in many cases. In particular, small laboratory flumes are able to generate regular sediment patterns, at Reynolds number of the order of, or below 100. This suggests a new approach to the problem: if turbulence is not essential to explain the formation of bars, braids and meanders, then laminar flumes become simple models of their natural turbulent counterparts. Our study presents the theoretical stability analysis of a laminar flume flowing over a sand substrate.   

Effect of Swirl on Flickering Motion of Diffusion Flame

The buoyancy-induced oscillation is referred to as the so-called flame flickering and its dynamics are important when revealing mechanism of flame oscillations encountered in some combustion systems. Many aspects of flame oscillation / buoyancy coupling have been extensively explored, but the effect of swirling flow on buoyancy-induced flame flickering has yet to be elucidated. The purpose of the present study is to investigate how the buoyancy-induced flame flickering motion is altered by swirl, using a rotating Bunsen burner. The rotating burner tube (Diameter of the burner tube D$_0$ is 10 mm) is vertically supported by bearings, and rotated by a DC motor through a pulley and belt unit. The fuel injection velocity U (= volume flow rate / cross-sectional area of the burner tube) is varied from 0.1 to 0.3 m/s. The rotational speed of the burner tube N is varied up to 2000 rpm. Variations in the flame motion, oscillation frequency, and flame height as a function of burner rotation rate are presented in detail.   

Micro-convection induced by the mass flux at the interface of a dissolving particle.

The classical general equations modeling mass transfer between a solid particle and ambient fluid medium are normally simplified and the means of simplification are different for gaseous and liquid medium. The major part of the works considering diffusion in liquids are based on the assumption of an infinitely diluted solution, which implies that no mechanical properties of the solution, including its density, depends on concentration, while the concentration flux satisfies the first Fick's law. Under this assumption, the velocity field is independent from the concentration, which is determined for a given velocity field from the convection-diffusion equation. However, when a particle is suspended in the otherwise quiescent fluid the flow is induced solely by the intensive mass transfer (which is typical at the initial stages of dissolution), or when the external flow and the natural convection are of comparable intensity, the approximation of diluted solution is not applicable. The mass transfer of a solid particle in these situations, which are typical for microgravity conditions and for nearly neutrally buoyant inclusions, is the main subject of the present communication. The use was made of the micro-convection model, based on the assumption that the density of the mixture depends solely on concentration. Spherically symmetric stationary and transient solutions were constructed and analyzed.   

A seamless multiscale model coupling dissipative particle dynamics and molecular dynamics

Dissipative particle dynamics (DPD) is a mesoscopic method in which coarse-graining is done at the molecular level to capture physics at the mesolevel. DPD includes thermal fluctuations which are important at the lower scales of the mesolevel. This feature makes DPD an attractive choice for seamless multiscale simulations at the sub-micron level. In this work we propose a multiscale model coupling DPD and molecular dynamics (MD). We demonstrate the applicability of this model by a Poiseuille flow simulation in which MD is used in the region close to walls, while DPD is used to model the bulk fluid. Comparison of the simulation results with the analytical solution will be provided.   

Instability and Electroconvection at a Electrodialysis Membrane

Electrolyte layer covered electrodialysis membrane under constant drop of potensial is considered. Self-similar solution of one-dimensional problem for second kind elecroosmosis (overlimitiny current) is found. Using special decomposition method analytical asymptotic solution of the problem is obtained; limiting current for the self-similar solution \[ j_\ast =4/\sqrt \pi \approx 2.25. \] Hydrodinamic instability of this solution with respect to linear 2D-perturbations is studied for the full system of equations. In contract to the works of Rubinstein is found that the region of instability is finite with respect to the wavenumber $\alpha $, growth rate $\lambda (\alpha )$ has maximum at some $\alpha =\alpha _m $ and 1D-solution is stable for sufficiently short perturbations. Direct numerical simulation of the full system of equations with a special non-uniform finite-differential grid shows that filtering mechanism of the linear stability singles out from the initial white-noise perturbations the maximum growth rate mode with $\alpha =\alpha _m $. Secondary instability leads to chaostic flow.   

Numerical Studies of the Robustness the SRPF and DRPF Algorithms for the Control of Chaos when System Parameters Drift

Recursive Proportional Feedback (RPF)\footnote{Rollins textit{et al}, Phys. Rev. E \textbf{47}, R780 (1993).} is an algorithm for the control of chaotic systems of great utility and ease of use. Control coefficients are determined from pre- control sampling of the system dynamics. We have adapted this method, in the spirit of the Extended Time-Delay Autosynchronization (ETDAS) method\footnote{Scolar \textit{et al}, Phys. Rev. E \textbf{50}, 3245 (1994).}, to seek minimal change from each previous value. The two methods so derived, Simple Recursive Proportional Feedback (SRPF) and Doubly Recursive Proportional Feedback (DRPF) have been studied in numerical simulations to determine their robustness when system parameters, other than that used for feedback, drift over time. We present evidence of the range over which each algorithm displays robustness against drift.   

Reaction-Diffusion Model Simulations relevant to Modified Taylor-Couette Flow in Systems of Varying Length

Previously, we have observed a period-doubling cascade to chaos in Modified Taylor-Couette Flow with Hourglass Geometry\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).}. Such behavior had been predicted by The Reaction-Diffusion model\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} simulations. The chaotic formation of Taylor-Vortex pair formation was restricted to a very narrow band about the waist of the hourglass. It was suggested that with increasing lengths of systems, the chaotic region would expand. We present a battery of simulations to determine the variation of the size of the chaotic region with length, seeking the transition to spatio- temporal chaos.   

Dimensional Analysis of Taylor-Couette Flow with Hourglass Geometry in both Laminar and Turbulent Regimes

Previously we have presented preliminary measurements indicating that the irregular generation of new Taylor Vortex Pairs in laminar Taylor-Couette flow with hourglass geometry could be characterized as low dimensional chaos\footnote{T. Olsen, R. Bjorge, \& R. Wiener, Bull. Am. Phys. Soc. \textbf{47-10}, 76 (2002).} and in the corresponding case of turbulent flow the chaotic dimension was higher\footnote{T. Olsen, B. Tomlin, R. Bjorge, \& R. Wiener, Bull. Am. Phys. Soc. \textbf{48-10}, 111 (2003).}. We now present data from far more extended time series of the periods between vortex formation, confirming and extending our original results. We present confirmation of our computational methodology in other systems.   

Excitation Transfer and Diffusion Property in a very Weakly Excited Lithium Gas

The aim of this study is a quantal computation of the diffusion coefficient $D$ of excited lithium atoms Li(2p) in their parent gas Li(2s). The variation law of $D$ with temperature $T$ is also treated. The calculations are further extended to the determination of the excitation transfer cross section correlated with the process Li(2p)+Li(2s) $\rightarrow$ Li(2s)+Li (2p). To do so, we have constructed from recent RKR and/or ab initio data points the eight singlet and triplet potential energy curves through which an atom Li(2p) approaches Li(2s). In the short- and long-range regions, the data points are smoothly connected to the forms $\exp(-bR)$ and $1/R^{n},$ respectively. The phase shifts, obtained for each energy $E$ and angular momentum $l$ from the numerical integration of the radial wave equation, allow the calculation of the diffusion and excitation transfer cross sections $Q_{D}$ and $Q_{tr}$. Our results show that the weighted cross sections vary with energy like $E^{-1/2} $ and the diffusion coefficient is found of the form $D \sim AT/n$, with $n$ being the number density and $A$ a constant. A semi-classical method shows $Q_{D} \simeq 2Q_{tr}$ and points out that the long-range $R^{-3}$ forces are prominent in the diffusion of excited atoms in their parent gas.   

Isotopic and Symmetry Effects in the Collision of Atomic Helium

The thermophysical properties of a helium dilute gas at low and high temperatures are revisited with new and recent potential data points. The second virial coefficients are computed in order to assess the accuracy of the constructed He-He potentials. The results, mainly at high temperatures, are in a good agreement with the published values. The isotopic effects due to the presence of $^{4}$He and $^{3}$He atoms are also examined and the calculations of various transport parameters, namely diffusion, viscosity, and thermal conductivity, are extended to include the nuclear spins and the symmetry effects, which arise from the identity and indistinguishability of the colliding atoms.   

Corrected Diffusion Coefficient of Lithium in Helium and Helium in Lithium

The diffusion coefficients $D_{0}$ of ground and excited lithium atoms diffusing in a helium buffer gas are reviewed with new and reliable potentials. The calculations are performed quantum mechanically at low and moderate temperatures and the results are compared with published theoretical and experimental data. The diffusion coefficients of ground Li in He and ground He in Li are particularly considered by taking into account the first- order correction like $D=D_{0}(1+\epsilon)$.   

Self-Diffusion Coefficient of a Weakly Ionized Cesium Monatomic Gas. Symmetry Effects

The quantum-mechanical computation of the diffusion coefficient $D$ begins with the determination of the singlet and triplet potential-energy curves which, in this work, separate asymptotically to Cs(6s)+Cs(6s). The knowledge of these potentials should lead to the determination of the phase shifts. Ignoring the identity of the interacting atoms, the cross section effective in diffusion is calculated for one molecular symmetry and the coefficient of diffusion is determined according to the Chapman-Enskog method. In reality, the colliding atoms are identical. Thus, the wave function of the diatomic system should be symmetrized. In such a case, quantum mechanics leads to symmetric and antisymmetric diffusion cross sections, as described by Karstic and Schultz, and the average diffusion cross section is recalculated by considering the Cs nuclear spin and the statistical weight of each molecular state. The evaluation of the self-diffusion coefficient of a dilute Cs gas is in a first step carried out without considering the symmetry effects. The results are compared with those of Nieto de Castro et al. The variation law with temperature of $D$ are further analyzed when the symmetry effects are ignored/included.   

Can Diffuse Methods be Tolerated in Numerical Predictions of Interfacial Instability?

The role of interfacial smearing in numerical simulations of interfacial instability is addressed by means of Orr-Sommerfeld type analysis of two stratifed fluid flow problems; one involving a perfectly sharp interface, and one in which the jumps in viscosity and/or density are smeared over an interfacial region- parameterized by shape and steepness. The results, confirmed by direct numerical simulations that fully account for the (jump) boundary conditions, demonstrate that a sharp interface in shear-dominated flows is physically unique and its instability behavior cannot be matched however steep a discontinuity-smearing is employed. Moreover we conclude that in such cases the results of smearing are inherently non-convergent, and that consequently such results cannot be regarded as products of direct numerical simulations.   

Rapid experimental optimization of efficiency of rolling and pitching foils.

The search for highest efficiency for a given thrust is considered for rolling and pitching hydrofoils when no apriori knowledge of the characteristics is available. This is an alternative to knowledge of the unsteady flow field over the performance domain. The variables are frequency of foil roll and pitch, angles of roll, pitch, pitch bias and phase difference between roll and pitch, and the incoming flow speed. A downhill simplex method is used to search the variables to optimize efficiency. Roll and pitch torque and foil position sensors give efficiency. A simulated annealing term with a gradually reducing `temperature' helps avoid becoming stuck in a selection where the repeatability level of the data results in inaccurate minimum. The method converged in 50 cycles in 4 minutes for all random starting values each search being for two cycles. The optimized parameters agree with our methodical measurements. The rapidity of the optimization suggests that high efficiency in swimming and flying animals might be a common occurrence.   

On Origin of Low Frequency Oscillations in Ionosphere

The origin of the observed low frequency oscillations in the ionosphere is a subject of much discussions in recent times. It is usually believed that the sheared parallel flow excites many plasma instabilities and these are responsible for the observed oscillations in the ionosphere. However, in this work we show that taking parallel curvature (second radial derivative) into account can change the picture all together. Parallel flow now (depending on the sign of the flow curvature) can act to stabilize or destabilize the modes. The theory of the origin of the low frequency oscillations therefore needs to be revisited in the new scenario.   

A Particle-Substrate Model and Its Applications to Cooling and Driven Granular Systems

A complete understanding of the microscopic dynamics of a monolayer of identical spheres moving on a substrate must encompass the effects of collisions and the substrate on the particles. We begin from first principles by considering collections of spherical frictional particles that roll and slip on a flat static substrate. We present a numerical model which accounts for collisional and surface frictional dissipation and their influence on particle dynamics for a quasi 2-dimensional cooling granular material. We apply this model to a simulation of the granular collider experiment (Painter et al., Physica D (2003)), in which collections of particles collided as they moved radially inward on a substrate. We find an agreement between the experimental and numerical results. We extend this model further to study a horizontally vibrated particle-substrate system. We show that the ratio of the substrate acceleration to the particle-substrate static frictional force (Kondic, Phys Rev. E (1999)) dominates the individual particle dynamics and the collision dynamics. We will present results from our numerical experiments which further higlight the critical role of static friction, relative to the driving acceleration.   

Excavation of sand by impinging jets of gas, with application to lunar landings

The erosion of sand by jets of gas is dominated in many cases by an interesting bulk flow of the granular material beneath the surface that occurs when the volumetric drag of gases diffusing through the porous medium produces a shear stress sufficient to unjam the material. Prior studies of rocket-induced cratering of a planetary surface had failed to identify this type of granular flow, which we are calling ``diffusion-driven shearing'' (DDS). It explains the simple observation that a crater is deepest in the center, despite the fact that the gases are stagnant directly beneath the center of the jet so that the traditional erosion mechanisms cannot possibly occur there, and despite the fact that the stagnation pressure under the jet is generally insufficient to cause the material to unjam. This study has also worked out a number of the scaling laws for the observed logarithmic growth of crater depth and width, and has explained the feedback mechanisms that govern that growth. The results are applied to controlling the blast effects of landing rockets on the Moon.   

Identifying and Addressing Student Difficulties with Hydrostatic pressure

This talk describes an investigation of student learning of the concept of pressure in a static liquid. We document patterns of student answers and explanations in response to a variety of written and interview questions. Our results suggest that many students in undergraduate physics courses fail to develop a correct understanding of the concept of pressure in the context of a static liquid. Many students have difficulty identifying the forces that act on a liquid and in relating those forces to pressure. We describe the development and assessment of research-based instructional materials designed to address student difficulties with pressure and provide evidence that these materials can improve student understanding of some ideas.   

Unsteady Interaction between a High-Pressure Turbine and a Counter-Rotating Low-Pressure Turbine

In an effort to strengthen our knowledge, understanding and prediction capabilities of unsteady turbine aerodynamics in multi-stage turbomachinery, an in-depth numerical analysis of a single stage High-Pressure Turbine (HPT) followed by a counter-rotating Low-Pressure Turbine (LPT) is performed via unsteady CFD using a parallel version of the RANS flow solver MSU-Turbo. Results from two numerical simulations are presented. Two HPT rotor design are being compared to each other and to available experimental data. The computational domains consist of the 1$^{st}$ HPT rotor blade, the 1$^{st}$ LPT nozzle, and the 1$^{st}$ counter-rotating LPT rotor. In order to respect the circumferential blade count and the corresponding spatial periodicity, a 1/18$^{th}$ of annulus is used for each blade row. Particular attention is given to the aerodynamic loss mechanism in the inter-turbine space. The inquiry focuses on the HPT rotor tail shock waves and their interaction with the LPT reflected shock. In addition, the investigation is extended to show how far downstream the interaction loss transfers to LPT components. Finally, an attempt is made to answer the following questions: 1)-Is the interaction loss reflected by time-averaged performance parameters? 2)- Is it carried by periodic waveforms? Or 3)- Is it represented by an increase of turbulence level?   

Large Eddy Simulation and PIV Visualization of a Vertical Hydrogen Jet

Increasing concerns about green house gas emissions and deteriorating local air quality will necessitate substantial emission reductions, particularly from road vehicles. Canada has made important contributions in paving the way for the use of hydrogen in the transportation sector, which could lead to a substantial reduction of urban pollution and CO2 emissions. However production and storage issues, as well as the absence of specific standards for hydrogen are regarded as obstacles to the introduction of hydrogen in the energy market. A hydrogen jet exiting into quiescent air in both the supersonic and subsonic regimes is simulated using large eddy simulation with a Smagorinski subgrid model. The subsonic results are compared with experimental results obtained by Panchapakesan et al. and So et al. Using a high speed PIV system, a subsonic air-in-air jet is studied and the time averaged flow-field is compared to the one obtained in the simulation.   

Experimental Results from a Flat Plate, Turbulent Boundary Layer Modified for the Purpose of Drag Reduction

Recent experiments on a flat plate, turbulent boundary layer at high Reynolds numbers ($>10^7$) were performed to investigate various methods of reducing skin friction drag. The methods used involved injecting either air or a polymer solution into the boundary layer through a slot injector. Two slot injectors were mounted on the model with one located 1.4 meters downstream of the nose and the second located 3.75 meters downstream. This allowed for some synergetic experiments to be performed by varying the injections from each slot and comparing the skin friction along the plate. Skin friction measurements were made with 6 shear stress sensors flush mounted along the stream-wise direction of the model.